背景:利用maximumlikelihood expectation maximization (MLEM)方法重建正子斷層掃描(PET)影像，其結果比 常規所使用的濾波反投影法(filteredback pr句ection; FBP) 更為精確。但在重建過程中，需要利用機率矩陣(probability matrix)來計算期望值。由於它的矩陣非常大，增加 儲存及運算的困難，而且它的建立需利用點射源對所有field of view (FOV)內各像素點逐一掃描，非常費時。本 研究旨在發展一新的機率記錄方式，以大幅縮小機率矩陣的大小。
方法:本研究提出新的機率矩陣，利用PET掃描儀的環式偵檢器與像素之間的對稱關係，減少矩陣中冗餘的部分。以簡化之矩陣代入MLEM方法用於2DHoffman數位 假體的模擬資料與PC-4096-15WBPET的實際點射源資料 之重建，評估用新機率矩陣重建後的影像品質。
結果:機率矩陣大小縮減為原本的1/n2 (n2為影像像素數 目)，運用此機率矩陣重建的影像，其影像品質並未受影響。矩陣的產生僅需要兩次線射源的掃描。
結論:新的機率矩陣能大量縮減其儲存空間及校正時間。

Background: The maximum likelihood expectation maximization (MLEM) method for PET reconstruction is more accurate than the conventional filtered backprojection (FBP) algorithm. However， the probability matrix is huge and its generation requires the scan of a point source moving through every location inside the FOY. The purpose of this study is to develop a method to reduce the size of the probability matrix for a ring system to improve the iterative speed of statistical reconstruction.
Methods: We utilized the geometric relationship between the pixel and detector pairs in the ring to factorize the probability matrix into two smaller independent matrices and reduce the matrix size significantly. A simulated 2D Hoffman digital phantom data and a real line source data from PC-4096-15WB PET scanning were used to assess the image quality of the MLEM reconstruction incorporating the new probability matrix.
Results: The size of the simplified probability matrices are reduced by a factor of ri. The reconstructed images of this method do not show any deterioration in the quality. It is feasible to generate the probability matrix using only two scans of line sources.
Conclusion: The new method reduces storage requirement without affecting image quality. The generation of probability matrix is greatly simplified.